Probabilistic Optimal Power Flow Considering the Dependence of Multiple Wind Farms Using Pair Diffusive Kernel Copula

As wind farms are commonly installed in areas with abundant wind resources,spatial dependence of wind speed among nearby wind farms should be considered when modeling a power system with large-scale wind power.In this paper,a novel bivariate non-parametric copula,and a bivariate diffusive kernel(BDK)copula are proposed to formulate the dependence between random variables.BDK copula is then applied to higher dimension using the pair-copula method and is named as pair diffusive kernel(PDK)copula,offering flexibility to formulate the complicated dependent structure of multiple random variables.Also,a quasi-Monte Carlo method is elaborated in the sampling procedure based on the combination of the Sobol sequence and the Rosen-blatt transformation of the PDK copula,to generate correlated wind speed samples.The proposed method is applied to solve probabilistic optimal power flow(POPF)problems.The effectiveness of the BDK copula is validated in copula definitions.Then,three different data sets are used in various goodness-of-fit tests to verify the superior performance of the PDK copula,which facilitates in formulating the dependence structure of wind speeds at different wind farms.Furthermore,samples obtained from the PDK copula are used to solve POPF problems,which are modeled on three modified IEEE 57-bus power systems.Compared to the Gaussian,T,and parametric-pair copulas,the results obtained from the PDK copula are superior in formulating the complicated dependence,thus solving POPF problems.

Unified probabilistic gas and power flow

The natural gas system and electricity system are coupled tightly by gas turbines in an integrated energy system. The uncertainties of one system will not only threaten its own safe operation but also be likely to have a significant impact on the other. Therefore, it is necessary to study the variation of state variables when random fluctuations emerge in the coupled system. In this paper, a multislack-bus model is proposed to calculate the power and gas flow in the coupled system. A unified probabilistic power and gas flow calculation, in which the cumulant method and Gram–Charlier expansion are applied, is first presented to obtain the distribution of state variables after considering the effects of uncertain factors. When the variation range of random factors is too large, a new method of piecewise linearization is put forward to achieve a better fitting precision of probability distribution. Compared to the Monte Carlo method, the proposed method can reduce computation time greatly while reaching a satisfactory accuracy.The validity of the proposed methods is verified in a coupled system that consists of a 15-node natural gas system and the IEEE case24 power system.

Probabilistic Optimal Power Flow of an AC/DC System with a Multiport Current Flow Controller

To evaluate the impact of the randomness and correlation of photovoltaic(PV)and load on AC/DC systems with a multiport current flow controller(M-CFC),this paper proposes a probabilistic optimal power flow calculation for AC/DC systems,based on a nonparametric kernel density estimation.First,according to the M-CFC model,the DC power flow calculation method with M-CFC was inferred,and its influence on line loss was analyzed.Second,a nonparametric kernel density estimation with an adaptive bandwidth is used to accurately describe the probability distribution of the PV and load,and correlation samples of the PV and load are obtained by the mixed copula function.Then an optimization model that considers system loss and static security is established,and a fast nondominated sorting genetic algorithm based on the elite strategy(NSGA-II)is used to calculate the multi-objective probability optimal power flow of the AC/DC system.Finally,a case study is performed on a modified IEEE39 bus system using measured PV and load data.We verified that the nonparametric kernel density estimation with an adaptive bandwidth can better adapt to random component uncertainty,and M-CFC can improve the static security of the system.